\relax 
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\citation{Emerson2005}
\citation{Emerson2005}
\citation{Emerson2007}
\citation{Dankert2009}
\newlabel{FirstPage}{{}{1}{\relax }{section*.1}{}}
\@writefile{toc}{\contentsline {title}{Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-qubit Quantum Processor}{1}{section*.2}}
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Introduction.}{1}{section*.3}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Theory.}{1}{section*.4}}
\newlabel{average_fidelity}{{1}{1}{\relax }{equation.0.1}{}}
\newlabel{average_Harr}{{3}{1}{\relax }{equation.0.3}{}}
\citation{Aaronson2004}
\citation{Bravyi2005}
\citation{Moussa2012}
\citation{Alex2013}
\citation{Venkatesh2012}
\citation{Knill2000}
\citation{Knill2000}
\citation{Knill2000}
\newlabel{average_Clifford}{{4}{2}{\relax }{equation.0.4}{}}
\newlabel{remain_signal}{{5}{2}{\relax }{equation.0.5}{}}
\newlabel{final_fidelity}{{6}{2}{\relax }{equation.0.6}{}}
\newlabel{Hoeffding}{{7}{2}{\relax }{equation.0.7}{}}
\newlabel{exp_number}{{8}{2}{\relax }{equation.0.8}{}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Experiment.}{2}{section*.5}}
\newlabel{decomp}{{9}{2}{\relax }{equation.0.9}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \relax \fontsize  {8}{9.5pt}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \belowdisplayskip \abovedisplayskip \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \topsep 4\p@ plus2\p@ minus2\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }{(color online). (a) Circuit for twirling procedure based on the Clifford group $\mathcal  {C}$. $\mathaccentV {tilde}07E{\mathcal  {U}} = \Lambda \circ \mathcal  {U}$ is the superoperator to describe the desired unitary $\mathcal  {U}$ associated with some noise $\Lambda $. $M_\psi $ and $M_{\psi , \mathcal  {C}_i, \mathcal  {U}}$ are the original and modified measurement operators, respectively. In this protocol $\text  {P}_1, \text  {P}_2$ and $\text  {P}_3$ are all Pauli operators and can be computed efficiently. (b) Molecular structure of Dichloro-cyclobutanone, where C$_1$ to C$_7$ form a 7-qubit system. (c) Pulse sequence for the creation of labeled PPS via the method in Ref. \cite  {Knill2000}. It consists of three parts: encoding, coherence selection (CS) and decoding. $\mathcal  {U}_{C}$, realized by a 80ms GRAPE pulse, is the Clifford gate to be certified. The instantaneous states are (unnormalized) $\rho _1 = \sigma ^7_z$, $\rho _2 = \sigma ^1_z\sigma ^2_z\cdots  \sigma ^7_z$, $\rho _3 = |00\cdots  0\delimiter "526930B \delimiter "426830A 00\cdots  0|+|11\cdots  1\delimiter "526930B \delimiter "426830A 11\cdots  1|$, and $\rho _4 = |00\cdots  0\delimiter "526930B \delimiter "426830A 00\cdots  0| \DOTSB \bigotimes@ \slimits@ \sigma ^7_z$, respectively. (d) Experimental result for the certification of $\mathcal  {U}_{C}$. $k$ is the number of Pauli operators for a designated weight $w$, while $k_w$ is the number of experiments via the sampling; $t$ is the typical time for the input Pauli state preparation, and $F_i$ is the calibration to capture the errors in preparation and measurement; $F_e$ is the experimental result of the probability of no error, and $F_{d,c}$ is the same quantity but without decoherence effect $E_d$. (e) Relationship among the experimental average fidelities (blue), decoherence effects (orange) and gate imperfections (gray) for different $w$.}}}{3}{figure.1}}
\newlabel{everything}{{1}{3}{\footnotesize {(color online). (a) Circuit for twirling procedure based on the Clifford group $\mathcal {C}$. $\tilde {\mathcal {U}} = \Lambda \circ \mathcal {U}$ is the superoperator to describe the desired unitary $\mathcal {U}$ associated with some noise $\Lambda $. $M_\psi $ and $M_{\psi , \mathcal {C}_i, \mathcal {U}}$ are the original and modified measurement operators, respectively. In this protocol $\text {P}_1, \text {P}_2$ and $\text {P}_3$ are all Pauli operators and can be computed efficiently. (b) Molecular structure of Dichloro-cyclobutanone, where C$_1$ to C$_7$ form a 7-qubit system. (c) Pulse sequence for the creation of labeled PPS via the method in Ref. \cite {Knill2000}. It consists of three parts: encoding, coherence selection (CS) and decoding. $\mathcal {U}_{C}$, realized by a 80ms GRAPE pulse, is the Clifford gate to be certified. The instantaneous states are (unnormalized) $\rho _1 = \sigma ^7_z$, $\rho _2 = \sigma ^1_z\sigma ^2_z\cdots \sigma ^7_z$, $\rho _3 = \ket {00\cdots 0}\bra {00\cdots 0}+\ket {11\cdots 1}\bra {11\cdots 1}$, and $\rho _4 = \ket {00\cdots 0}\bra {00\cdots 0} \bigotimes \sigma ^7_z$, respectively. (d) Experimental result for the certification of $\mathcal {U}_{C}$. $k$ is the number of Pauli operators for a designated weight $w$, while $k_w$ is the number of experiments via the sampling; $t$ is the typical time for the input Pauli state preparation, and $F_i$ is the calibration to capture the errors in preparation and measurement; $F_e$ is the experimental result of the probability of no error, and $F_{d,c}$ is the same quantity but without decoherence effect $E_d$. (e) Relationship among the experimental average fidelities (blue), decoherence effects (orange) and gate imperfections (gray) for different $w$.}\relax }{figure.1}{}}
\newlabel{Hamiltonian}{{10}{3}{\relax }{equation.0.10}{}}
\citation{Ryan2008}
\citation{Khaneja2005}
\citation{Weinstein2004}
\citation{Vandersypen2001}
\bibcite{Moussa2012}{{1}{}{{}}{{}}}
\bibcite{Emerson2005}{{2}{}{{}}{{}}}
\bibcite{Emerson2007}{{3}{}{{}}{{}}}
\bibcite{Dankert2009}{{4}{}{{}}{{}}}
\bibcite{Aaronson2004}{{5}{}{{}}{{}}}
\bibcite{Bravyi2005}{{6}{}{{}}{{}}}
\bibcite{Alex2013}{{7}{}{{}}{{}}}
\bibcite{Venkatesh2012}{{8}{}{{}}{{}}}
\bibcite{Knill2000}{{9}{}{{}}{{}}}
\bibcite{Ryan2008}{{10}{}{{}}{{}}}
\bibcite{Khaneja2005}{{11}{}{{}}{{}}}
\bibcite{Weinstein2004}{{12}{}{{}}{{}}}
\bibcite{Vandersypen2001}{{13}{}{{}}{{}}}
\bibdata{twirlingNotes}
\bibstyle{apsrev4-1}
\citation{REVTEX41Control}
\citation{apsrev41Control}
\providecommand\NAT@force@numbers{}\NAT@force@numbers
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Conclusion.}{4}{section*.6}}
\@writefile{toc}{\contentsline {section}{\numberline {}References}{4}{section*.7}}
\newlabel{LastBibItem}{{13}{4}{\relax }{section*.7}{}}
\newlabel{LastPage}{{}{4}{}{}{}}
